Subspace topology: Difference between revisions
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In [[general topology]], the '''subspace topology''', or '''induced''' or '''relative''' topology, is the assignment of open sets to a [[subset]] of a [[topological space]]. | In [[general topology]], the '''subspace topology''', or '''induced''' or '''relative''' topology, is the assignment of open sets to a [[subset]] of a [[topological space]]. | ||
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==References== | ==References== | ||
* {{cite book | author=Wolfgang Franz | title=General Topology | publisher=Harrap | year=1967 | pages=36 }} | * {{cite book | author=Wolfgang Franz | title=General Topology | publisher=Harrap | year=1967 | pages=36 }} | ||
* {{cite book | author=J.L. Kelley | authorlink=John L. Kelley | title=General topology | publisher=van Nostrand | year= 1955 | pages=50-53 }} | * {{cite book | author=J.L. Kelley | authorlink=John L. Kelley | title=General topology | publisher=van Nostrand | year= 1955 | pages=50-53 }}[[Category:Suggestion Bot Tag]] | ||
Latest revision as of 06:01, 23 October 2024
In general topology, the subspace topology, or induced or relative topology, is the assignment of open sets to a subset of a topological space.
Let (X,T) be a topological space with T the family of open sets, and let A be a subset of X. The subspace topology on A is the family
The subspace topology makes the inclusion map A → X continuous and is the coarsest topology with that property.
References
- Wolfgang Franz (1967). General Topology. Harrap, 36.
- J.L. Kelley (1955). General topology. van Nostrand, 50-53.